Lorentz contraction of box filled with gas

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The discussion centers on the behavior of a gas-filled box when accelerated, particularly regarding Lorentz contraction and pressure changes. It is established that while the box experiences length contraction from an external observer's perspective, the pressure inside remains constant in the box's own frame due to the principles of relativity. The calculations demonstrate that the force exerted by gas molecules is reduced by a factor of gamma, and this reduction balances with the contraction of the box's area, leading to no change in pressure. The conversation also touches on the implications of these principles for solid materials, suggesting that Lorentz contraction does not induce stress in materials in the same way it does in gases. Overall, the pressure and volume of the gas are invariant in the box's reference frame, emphasizing the relativity of motion.
  • #121
AVentura said:
thanks, I have been thinking about this for years but didn't know what it was called. (they didn't cover this in my master's program)

but I don't think most Physicist would agree with Bell (none of my professors would have). I got in lots of arguments.

The wikipedia entry on Bell's spaceships paradox says that CERN put together a think tank that disagreed with Bell. What was there argument?

The wikipedia article goes on to quote Bell as saying "Of course, many people who get the wrong answer at first get the right answer on further reflection".

I am not sure what the argument the CERN scientist's had for assuming the string would not break besides the counter intuitive notion that a physical object between the spaceships length contracts while the space between them does not. That is quite shocking to some people that view length contraction as a mathematical entity rather than a physical one.

The wikipedia article also states a paper by Matsuda and Kins-hita contradicting Bell's conclusion met with much criticism.

Here is my simple explanation of Bell's spaceship paradox if you are interested.

Say we have 2 stationary rockets a distance x apart. A ruler is attached to one rocket and extends to touch the other rocket but is not attached to the second rocket. The 2 rockets launch simultaneously from A's frame with constant and equal proper acceleration and maintaining the same separation in A's frame. (A does not accelerate). Now let's say they stop accelerating simultaneously in A's frame at a final and equal velocity of v=0.8. The distance between the 2 rockets is x according to A and the ruler is now length contacted to 0.6x. If the ruler is now stretched in an attempt to connect it to both rockets its going break, right?

To an observer that was always moving at 0.8c relative to observer A, the rockets do not take off simultaneously but the front rocket appears to take off before the rear rocket. With the rear rocket stationary and the front rocket accelerating it is obvious that if the ruler was attached to both rockets it would be under a lot of strain and will eventually snap.

The arguments for why an object connecting both rockets will eventually snap are so simple and clear, it is difficult to imagine why anyone would disagree.
 
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  • #122
aventura:

i presume what you are asking me is whether i believe that length contraction is real or just an illusion. it is real for an object that is really moving.
 
  • #123
granpa,
well suppose you could communicate instantly with any part of the universe or at least with arbitrarily small delay. that would allow you to know the absolute time.

if you know absolute time then you should be able to determine absolute velocity simply by looking at your time dilation.

https://www.physicsforums.com/showthread.php?t=235621

of course, there is no way to do either. some people do suggest that quantum entanglement might allow ftl communication but the consensus seems to be that it can't.
Thanks for pointing that out. But it only needs arbitrarily fast communcation, not ftl.

What do you mean by 'really moving' in your post above ?
 
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  • #124
arbitrarily fast communcation, not ftl?

arbitrarily fast is a way of saying virtually infinitely fast. how is that not ftl?

in other words, be able to communicate with any part of the universe with arbitrarily small delay (ie. virtually zero delay).
 
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  • #125
granpa,
yes, sorry, I meant to say not instantaneous ( it's sunday afternoon ! ).

But you didn't answer my question. I'm not challenging you, you've pointed out some interesting things so far.
 
  • #126
https://www.physicsforums.com/showthread.php?t=235621

both twins perceive the other to be time dilated but in reality it is only the one that is really moving that is time dilated. once he stops he realizes this. same with length contraction.

that was weird. when i first viewed it my post was blinking solid black. never seen that before.
 
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  • #127
granpa,
OK. I suppose you could say 'the one who is off the free-fall geodesic', or 'has his engines on'.
This getting off-topic, so I'll leave it there.

M
 
  • #128
kev said:
The wikipedia article goes on to quote Bell as saying "Of course, many people who get the wrong answer at first get the right answer on further reflection".

I am not sure what the argument the CERN scientist's had for assuming the string would not break besides the counter intuitive notion that a physical object between the spaceships length contracts while the space between them does not. That is quite shocking to some people that view length contraction as a mathematical entity rather than a physical one.

The wikipedia article also states a paper by Matsuda and Kins-hita contradicting Bell's conclusion met with much criticism.

Here is my simple explanation of Bell's spaceship paradox if you are interested.

Say we have 2 stationary rockets a distance x apart. A ruler is attached to one rocket and extends to touch the other rocket but is not attached to the second rocket. The 2 rockets launch simultaneously from A's frame with constant and equal proper acceleration and maintaining the same separation in A's frame. (A does not accelerate). Now let's say they stop accelerating simultaneously in A's frame at a final and equal velocity of v=0.8. The distance between the 2 rockets is x according to A and the ruler is now length contacted to 0.6x. If the ruler is now stretched in an attempt to connect it to both rockets its going break, right?

To an observer that was always moving at 0.8c relative to observer A, the rockets do not take off simultaneously but the front rocket appears to take off before the rear rocket. With the rear rocket stationary and the front rocket accelerating it is obvious that if the ruler was attached to both rockets it would be under a lot of strain and will eventually snap.

The arguments for why an object connecting both rockets will eventually snap are so simple and clear, it is difficult to imagine why anyone would disagree.

So the ruler is now length contacted while the distance between the 2 rockets does not change.
How about the gas in the box? Would the distance between gas particles change or not while the box is length contacted? In other words, would the box compress the gas in it?
 
  • #129
the box occupies less space but isn't compressed. to the box nothing appears to have changed.
 
  • #130
Qeinstein said:
So the ruler is now length contacted while the distance between the 2 rockets does not change.
How about the gas in the box? Would the distance between gas particles change or not while the box is length contacted? In other words, would the box compress the gas in it?

just to the initial observer. to that person, the particles would be happy to get closer together without any extra force. their fields are compressed in that direction.
 
  • #131
thats right. and that brings up the interesting fact that electric and magnetic fields themselves possesses velocity.
 
  • #132
it's also important to remember that some observers in different frames can see the box stretched (perhaps they see it getting closer to their velocity) They would see a different set of fields that make sense with this.
 
  • #133
kev said:
The wikipedia article also states a paper by Matsuda and Kins-hita contradicting Bell's conclusion met with much criticism.

no, they agree with Bell (it is linked from wikipedia). they leave out the string and just ask if the ships contract (no they say)
so they and Bell were met with criticism.

but i would tell the critics this:
I work in a radiation therapy department with 2 linear accelerators that are 1 meter in length but are 20 meters apart (co-linear acceleration). The amount of length contraction expected at these speeds can be significant (0.5). That would put the electrons in the hall where I'm standing! Imagine physicists in Cal Tech and MIT that just happened to accelerate electrons in the same direction at the same time. Would they contract to Nebraska?
 
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  • #134
AVentura said:
just to the initial observer. to that person, the particles would be happy to get closer together without any extra force. their fields are compressed in that direction.

Can you tell me why the distance between the gas particles would change but the distance between the rocket ships won't change?
 
  • #135
the gas particles are pressing off one another, but are bound by the box. the gas particles don't mind getting closer together in the direction of acceleration. at the same time the box is contracting in the direction of acceleration. so it's a nice point that you have made. contraction can occur whenever particles are in some sort of interaction, not just a solid state lattice.

are the ships in some sort of interaction? well, there is gravity. something must be keeping them apart for them to float in space like that. perhaps they are bouncing photons off one another to stay separated. that system may contract under acceleration. i really don't understand gravity honestly. it seems like such a system really includes everything in the universe, and would have to be solved as such.

but the electrons in my linacs are not interacting (or I am overcoming it). and I think that is what Bell intended. even if there is an attraction it is accounted for by some system that keeps the ships with the same acceleration relative to a stationary ruler at rest alongside the ships.

in other words, ships don't contract when we don't let them. seems like a real stupid statement, and it is.

but if you did this, and had a string between them, half the scientific world would be in for a shock, and the other half would make a toast. because this is what has never been done so far. someday, someday.
 
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  • #136
AVentura said:
no, they agree with Bell (it is linked from wikipedia). they leave out the string and just ask if the ships contract (no they say)
so they and Bell were met with criticism.

Your right, the Japenese scientists were agreeing with Bell. More precisely they ask "Does the space (distance) between two ships contract?" and later state "One can conclude that the length of each spaceship may contract according to Eq. (1) but that the distance between the two spaceships should stay constant, as viewed from S."

At the time they seemed to get even more criticism than Bell which made me assume they were disagreeing with Bell. The summary of their paper says:

"After our Japanese papers and a few papers criticizing our argument
appeared in the Japanese physics journal “Parity,” we
discovered that a very similar argument was discussed by Bell,
and that it was met with similar criticism that we are [1]. This
means that, unfortunately, many physicists did not, have not
and still do not understand the real meaning of the Lorentz
contraction even after almost 100 years of the introduction of
special relativity by Einstein."

That is a bit worrying...:rolleyes: Are modern scientists so steeped in abstract concepts that they find simple physical concepts difficult to relate to?
 
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  • #137
kev said:
That is a bit worrying...:rolleyes: Are modern scientists so steeped in abstract concepts that they find simple physical concepts difficult to relate to?

my university experience says yes.
 
  • #138
AVentura said:
my university experience says yes.

I probably shouldn't appeal to authority, but it may be worth mentioning that the John Bell the spaceship paradox was named after is the same John bell that came up with Bell's inequalities which has been described as one one of the most profound discoveries of science.
 
  • #139
Hello again granpa.

Quote:-
----relativity does not say that there is no absolute velocity. it just says that you can't determine what it is without ftl travel.----

So relativity does not deny the existence of absolute velocity we just need FTL travel. This can only be information travel as material and EM FTL is not allowed in SR

Absolute time be determined if we have FTL transmission of information.

So knowing this absolute time, by some method we determine absolute velocity.

OK.

So with instantaneous transmission of information ( it has to be instantaneous or we are back to some finite velocity such as c ) we can synchronize all the clocks in our own frame without need for allowing for transmission time or worrying about the anistropy of c. So can everybody else in their own frame. How does this single out a unique absolute rest frame. ( i say rest frame when i should really say frame with absolute velocity zero ).

If we still have the requirement, which SR has, that c is the same for all observers we are still back to where we started. Every observer in relative inertial motion will observe time dilation in the other's frame. We still cannot tell who is " really " moving. This is a consequence of c being the same for all inertial observers.

If you have a valid theory you will need to spell it out in detail for me to understand as i may be making invalid assumptions about your reasoning or my understanding of basic SR may be at fault.

Thankyou in advance for your more detailed explanation. If you can convince me i will happily concede that i am wrong. It won't be the first time.

Matheinste.
 
  • #140
Hello again granpa.

Quote:-
----relativity does not say that there is no absolute velocity. it just says that you can't determine what it is without ftl travel.----

So relativity does not deny the existence of absolute velocity we just need FTL travel. This can only be information travel as material and EM FTL is not allowed in SR

Absolute time be determined if we have FTL transmission of information.

So knowing this absolute time, by some method we determine absolute velocity.

OK.

So with instantaneous transmission of information ( it has to be instantaneous or we are back to some finite velocity such as c ) we can synchronize all the clocks in our own frame without need for allowing for transmission time or worrying about the anistropy of c. So can everybody else in their own frame. How does this single out a unique absolute rest frame. ( i say rest frame when i should really say frame with absolute velocity zero ).

If we still have the requirement, which SR has, that c is the same for all observers we are still back to where we started. Every observer in relative inertial motion will observe time dilation in the other's frame. We still cannot tell who is " really " moving. This is a consequence of c being the same for all inertial observers.

If you have a valid theory you will need to spell it out in detail for me to understand as i may be making invalid assumptions about your reasoning or my understanding of basic SR may be at fault.

Thankyou in advance for your more detailed explanation. If you can convince me i will happily concede that i am wrong. It won't be the first time.

Matheinste.
 
  • #141
well suppose you could communicate instantly with any part of the universe or at least with arbitrarily small delay. that would allow you to know the absolute time.

if you know absolute time then you should be able to determine absolute velocity simply by looking at your time dilation.

https://www.physicsforums.com/showthread.php?t=235621

of course, there is no way to do either. some people do suggest that quantum entanglement might allow ftl communication but the consensus seems to be that it cant.
 
  • #142
Hello granpa.

Quote:-
---if you know absolute time then you should be able to determine absolute velocity simply by looking at your time dilation.----

If you know absolute time, from instantaneous information transmission, then all clocks in all frames would presumably be synchronized to this time and remain so. In this case there would be no difference in anyones clocks whatever their relative motion ( presumably they would instantaneously be updated ) and hence no observable time dilation between frames. So how would this help to determine an absolute velocity or special frame.

You have merely quoted what you said before with no more helpful information. To help anyone understand what you are claiming please give a more detailed reasoning.

Matheinste
 
  • #143
sorry, your q makes no sense.
of course there is time dilation. look at the twin paradox here:

https://www.physicsforums.com/showthread.php?t=235621

the ability to communicate instantly with any part of the universe would make no difference to time dilation. the reason the moving twin sees the nonmoving twins clock ticking slower is because of loss of simultaneity. but if he can communicate instantly then he can see that all the line of clocks are in fact synchronized and running at twice his own rate (not 1/2 as he would otherwise believe). from that he can determine that he is time dilated. the nonmoving twin will see something completely different.

i edited my post after first posting it. i figured you simply didnt read the new version.
 
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  • #144
You could choose one clock, and all other clocks would take their time from it. This would give 'an' absolute time. All clocks would look to all observers to have the same time and rate. Paradoxical ?
 
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  • #145
the clocks might run at the same rate but will the natural processes in each frame run at the same rate? no.

all will indeed look to some central clock to determine what time it really it. proper time i guess. but each frame will still be time dilated. atoms will vibrate at lower rates, ect...
 
  • #146
granpa;
the clocks might run at the same rate but will the natural processes in each frame run at the same rate? no.

all will indeed look to some central clock to determine what time it really it. proper time i guess. but each frame will still be time dilated. atoms will vibrate at lower rates, etc..
Exactly, hence the paradox.

It's late, my computer is going to sleep now.

M
 
  • #147
thats not what the twin paradox is about.

and time dilation is not a paradox anyway.
 
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  • #148
Hello again.

How do you single out a frame that is special and thus determine absolute velocity, or rest. Picking out one frame at random and synchronizing all clocks to that frame ( which are alreadt synchronizes anyway )proves or achieves nothing.

Matheinste
 
  • #149
i just answered that. only the moving twin is actually time dilated. its true that he sees the nonmoving twin as being time dilated but that because of loss of simultaneity. if he can communicate instantly with any part of the universe then loss of simultaneity will not prevent him from seeing that the nonmoving twins clock is actually ticking at twice his own rate rather than 1/2 as he would otherwise believe.
 
  • #150
Hello again.

I'm sorry i'll have to give it more thought. It's 2.00AM here and I've got work tomorrow.

Goodnight.

Matheinste.
 

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